Crystalline vs amorphous solids, the four types of crystals, the unit cell and the seven crystal systems, cubic packing and allotropy — exam-focused for the BIEK / Sindh Board paper. Read it straight through, or open the interactive lecture and explore the unit-cell viewer.
1 — The solid state
In a solid the particles are packed closely in fixed positions and can only vibrate about those positions — they cannot move freely.
General properties of solids
- Definite shape and volume.
- Incompressible (almost no empty space) and high density.
- Particles vibrate but do not translate → solids are rigid.
- Strong intermolecular forces hold them in place.
- Very slow diffusion; do not flow.
2 — Crystalline vs amorphous solids
| Property | Crystalline | Amorphous |
|---|
| Arrangement | regular, repeating, long-range order | irregular, short-range order |
| Melting point | sharp, definite | melts over a range (softens) |
| Shape | definite geometric faces & angles | no regular shape |
| Nature (cleavage) | anisotropic; cleaves along planes | isotropic; irregular break |
| Examples | NaCl, diamond, quartz, ice | glass, rubber, plastic, tar |
Anisotropic = physical properties differ with direction (crystalline). Isotropic = same in all directions (amorphous & liquids). Amorphous solids are sometimes called super-cooled liquids.
3 — Types of crystalline solids
| Type | Particles & force | Properties | Example |
|---|
| Ionic | ions; electrostatic | hard, brittle, high m.p.; conduct when molten/aqueous | NaCl |
| Covalent (network) | atoms; covalent bonds | very hard, very high m.p.; non-conductors (except graphite) | diamond, SiO₂ |
| Molecular | molecules; van der Waals / H-bonds | soft, low m.p.; non-conductors | ice, I₂, dry ice |
| Metallic | cations in a "sea" of electrons | malleable, ductile, lustrous; good conductors | Cu, Fe, Na |
4 — Crystal lattice & unit cell
- Crystal lattice (space lattice) — the regular three-dimensional arrangement of points (each representing a particle) that repeats throughout a crystal.
- Unit cell — the smallest repeating unit of the lattice which, repeated in three dimensions, builds the whole crystal.
A unit cell is defined byedge lengths a, b, c and angles α, β, γ
5 — The seven crystal systems
All crystals fall into seven systems, classified by the relationship between the edges and angles of the unit cell.
| System | Edges | Angles | Example |
|---|
| Cubic | a = b = c | all 90° | NaCl |
| Tetragonal | a = b ≠ c | all 90° | SnO₂ |
| Orthorhombic | a ≠ b ≠ c | all 90° | rhombic S |
| Monoclinic | a ≠ b ≠ c | two 90°, one ≠ | monoclinic S |
| Triclinic | a ≠ b ≠ c | none 90° | CuSO₄·5H₂O |
| Hexagonal | a = b ≠ c | 90°, 90°, 120° | graphite |
| Rhombohedral | a = b = c | equal, ≠ 90° | calcite |
6 — Cubic unit cells & atoms per cell
The cubic system has three types. Counting the share of each atom gives the number of atoms per unit cell.
| Cubic type | Atom positions | Atoms / unit cell |
|---|
| Simple cubic (SC) | 8 corners | 8 × ⅛ = 1 |
| Body-centred (BCC) | 8 corners + 1 centre | (8 × ⅛) + 1 = 2 |
| Face-centred (FCC) | 8 corners + 6 faces | (8 × ⅛) + (6 × ½) = 4 |
Shares: a corner atom is shared by 8 cells (⅛ each); a face atom by 2 cells (½); an edge atom by 4 (¼); a body-centre atom belongs to 1 cell.
7 — Isomorphism & polymorphism
- Isomorphism — different substances with the same crystalline form (e.g. ZnSO₄·7H₂O and MgSO₄·7H₂O).
- Polymorphism — the same substance existing in more than one crystalline form (e.g. CaCO₃ as calcite and aragonite).
8 — Allotropy
- Allotropy — the existence of an element in two or more different physical forms in the same physical state.
Allotropes of carbon
| Allotrope | Bonding / structure | Property |
|---|
| Diamond | each C sp³, 3-D covalent network | hardest natural substance; non-conductor |
| Graphite | sp² layers, delocalised electrons | soft, slippery; conducts electricity |
| Fullerene (C₆₀) | closed cage of sp² carbons | molecular; "bucky-ball" |
9 — Lattice energy
- Lattice energy — the energy released when one mole of an ionic crystal is formed from its gaseous ions (or the energy needed to break it apart).
Higher charge and smaller ions → greater lattice energy → higher melting point. e.g. MgO > NaCl.
10 — Properties of crystalline solids
- Sharp melting point (ordered lattice, equal bond strengths).
- Cleavage — split cleanly along definite planes.
- Anisotropy — properties vary with direction.
- Definite geometric shape with characteristic interfacial angles.
11 — Worked & reasoning questions
atoms per cell
How many atoms are in a face-centred cubic (FCC) unit cell?
corners: 8 × ⅛ = 1; faces: 6 × ½ = 3 → total = 4 atoms
reasoning
Why does diamond not conduct electricity but graphite does?
In diamond all 4 valence electrons of each C are in covalent bonds (none free); in graphite each C uses only 3, leaving delocalised electrons → graphite conducts, diamond does not
reasoning
Why is glass called a super-cooled liquid?
It is amorphous (no long-range order) and softens over a range like a very viscous liquid → no sharp melting point
12 — Exam recap
- Properties of solids; crystalline vs amorphous (anisotropy/isotropy).
- Four types of crystals (ionic, covalent, molecular, metallic) & properties.
- Crystal lattice, unit cell (a, b, c, α, β, γ).
- The seven crystal systems.
- Cubic cells SC/BCC/FCC and atoms per cell (1, 2, 4).
- Isomorphism, polymorphism, allotropy; lattice energy.